
    sg_                        d dl mZ d dlmZ d dlmZmZ d dlmZm	Z	 d dl
mZ d dlmZmZmZmZmZmZ d dlmZ d dlmZmZ d d	lmZ d d
lmZmZmZ d dlmZm Z m!Z! d dl"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z. d dl/m0Z0m1Z1m2Z2 d dl3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZE d dlFmGZGmHZHmIZImJZJ d dlKmLZLmMZMmNZNmOZOmPZPmQZQ d dlRmSZSmTZTmUZU d dlVmWZW d dlXmYZYmZZZ d dl[m\Z\m]Z] d dl^m_Z_m`Z` d dlambZb d dlcmdZd d dlemfZf d dl[mgZg d dlhmiZi d dljmkZkmlZl d dlmmnZnmoZo d d lpmqZqmrZrmsZsmtZt  ed!d"d"#      Zud$ Zvd% Zwd& Zxd' Zyd( Zzd) Z{d* Z|d+ Z}d, Z~d- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8 Zd9 Zd: Zd; Zd< Zekd=        Zd> Zd? Zd@ ZdA ZdB ZdC ZdD ZdE ZdF ZdG ZdH ZdI ZdJ ZdK ZdL ZdM ZekdN        ZdO ZdP ZdQ ZdR ZdS ZdT ZdU ZdV ZekdW        ZdX ZdY ZdZ Zd[ Zd\ Zd] Zd^ Zd_ Zd` Zda Zdb Zdc Zdd Zde Zdf Zdg Zdh Zdi Zdj Zdk Zdl Zdm Zdn Zdo Zdp Zdq Zdr Zds Zdt Zdu Zdv Zdw Zdx Zdy Zdz Zd{ Zd| Zd} Zd~ Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zekd        Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdÄ ZdĄ Zdń ZdƄ ZdǄ ZdȄ ZdɄ Zdʄ Zd˄ Zd̄ Zd̈́ Zy)    )product)Sum)Functiondiff)
EulerGammaGoldenRatio)Mod)EIRationaloopizoo)S)Symbolsymbols)	fibonacci)binomial	factorialsubfactorial)Absresign)LambertWexplog)atanhasinhacoshacothacschasechtanhsinh)ceilingfloorfrac)cbrt	real_rootsqrt)	Piecewise)acosacotacscasecasinatancoscotcscsecsintan)besselibesselybesseljbesselk)Eierferfcerfifresnelcfresnels)digammagamma
uppergamma)meijerg)Integral	integrate)Limitlimit)
logcombinesimplify)hyperexpand)AccumBounds)Mul)
heuristics)Order)XFAILraises)
elliptic_e
elliptic_k)xyzknTintegerpositivec            	      \   t        t        t        t              t        u sJ t        t        t        t               t         u sJ t        t         t        t              t         u sJ t        t        dz  t        t               t        u sJ t        t        dz   t        t              t         u sJ t        t        t        t              z  t        dd      dk(  sJ t        dt        z  t        t              dk(  sJ t        t	        t              t        t              t        u sJ t        t	        t               t        t              t         u sJ t        t	        t              t        z  t        t              t        u sJ t        dt        z  t	        t               z
  t        t              dk(  sJ t        t        dt        z  z   t        t              t        u sJ t        t        t        dz  z
  t        t              t         u sJ t        dt        z   dt        d      z   z  t        d      dk(  sJ t        dt        z   t        z  t        d      t        t        dz   t        z  t        d      k(  sJ t        dt        z   t        z  t        dd      t        t        dz   t        z  t        dd      k(  sJ t        dt        z   t        z   t        z  t        dd      t        dt        z   t        z   t        z  t        dd      k(  sJ t        t        t        z  t        t              z  t        d      t         t        t              z  k(  sJ t        t        t        t        z         t        z  t        d      t        t        t                    t        z  k(  sJ t        t        dt        z  dz         t        t              dk(  sJ t        t        j                  t        t               t        j                  u sJ t        t        d      t        z  t        t        j                        t        j                  u sJ t        dt        dz
  z  t        dd      t        u sJ t        dt        dz
  z  t        dd      t         u sJ t        ddt        z
  dz  z  t        dd      t         u sJ t        ddt        z
  dz  z  t        dd      t        u sJ t        dt        t              z  t        t        d      t         u sJ t        dt        t              z  t        t        d      t        u sJ t        dt        t              z  t        t        dz  d      t         u sJ t        dt        t              z  t        t        dz  d      t        u sJ t        dt!        t        dz        z  t        dt        z  t#        dd      z  d      t        u sJ t        dt!        t        dz        z  t        dt        z  t#        dd      z  d      t         u sJ t        dt%        t              dz  z  t        t        t#        dd      z  d      t         u sJ t        dt%        t              dz  z  t        t        t#        dd      z  d      t        u sJ t        t!        t              t        t              t'        t        j(                  t        j*                        k(  sJ t        t%        t              t        t              t'        t        j(                  t        j*                        k(  sJ t        t-        t              t        t              t'        t        j(                  t        j*                        k(  sJ t        t/        t              t        t              t'        t        j(                  t        j*                        k(  sJ t        t        t              t        z  t        dd	      dk(  sJ t        t        dz  t        dd	      dk(  sJ t        dt        dz  z  t        dd	      t        u sJ t        dt        z  t        dd	      t0        u sJ t        ddt        z  z   t        d      t        u sJ t        ddt        z  z   t        dd      t         u sJ t        t        d
z  t        dd      t        u sJ t        t        dz  t        dd      t         u sJ t        dt        t              z  t        dd      t         t2        z  k(  sJ t        t        dz  t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t         z  t        dd      t         ddt        z
  z  z  k(  sJ t        dt        t              z   t        z  t        d      t        t        t              dz   t        z  t        d      k(  sJ t        dt5        t              z  t        dd      t        k(  sJ t        dt5        t              z  t        dd      t         k(  sJ t        dt7        t              z  t        dd      t        k(  sJ t        dt7        t              z  t        dd      t         k(  sJ t        t        dt        z        dt        t              z  z   t        dd      t        k(  sJ t        t        dt        z        dt        z  z   t        dd      t        k(  sJ y )N   r   +dir   -      +-)rI   rU   r   r   r   r*   rH   rV   r   r2   rC   r   NaNrP   r6   r   r7   r   r3   rM   NegativeInfinityInfinityr5   r4   r   r   r0   r$        Q/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_limits.pytest_basic1rp   )   s\   Ar?b   Ass"""!Qs"""Aq2#"$$$!Q$22#%%%3q61aS)Q...1a!!!QB2%%%#a&!R RC'''Q1b!R'''1sA2w2&!+++QqS!R B&&&QT1b!bS(((!a%1tAw;'A.!333!a%"a#ua!eb[!Q'????!a%"a,q1urk1aS0QQQQ!a%!)b!QC0E1q519r/1aUX4YYYY1SVQ"rc$q'k111QUAq!$SVR777qsQwB'1,,,B3155(((q!Q&!%%///AEAqc*b000AEAqc*rc111AEA:q!-"444AEA:q!-3333q61bc*rc1113q61bc*b0003q61bd,3333q61bd,2223q!t9a!B$!Q!7SARGGG3q!t9a!B$!Q!7SAbSHHH3q619a"Xa^"3#>2#EEE3q619a"Xa^"3#>"DDDQB;q/A/A1::#NNNNQB;q/A/A1::#NNNNQB;q/A/A1::#NNNNQB;q/A/A1::#NNNN Q1aT*a///Aq!&!+++1a4A4(B... 1a%,,, QqS!Q2%%% QqS!QC(RC///R!QC(B...R!QC(RC///47Aqc*sAg555Aq!%***a!QC(A---RCA3'B3a"f~+====!c!f*r!1a(E3q6A:2BAq,IIII 47Aq,22247Aq,33347Aq,22247Aq,333QqSAc!fH$a#6"<<<QqSAaCAS1R777rn   c                     t        t        t        z  t        dd      dk(  sJ t        t        t              dz
  t        z  t        d      dk(  sJ t        ddt        z  z   t        t              dk(  sJ t        t        dt        z         t        t              dk(  sJ t        t        t        t               z   t        t              t        u sJ t        t        t        t        dz         z   t        t              t        u sJ t        t        t        t        t                     z   t        t              t        u sJ t        ddt        z  z   t        t               z
  t        t              dk(  sJ y )Nr   r_   r`   rb   ri   r^      rI   rU   r   r   rm   rn   ro   test_basic2rt   p   s   Aq!%***#a&1*aA&!+++QqS!R A%%%#ac(Ar"b(((S!Wa$***S!Q$ZB'2---S#a&\!1b)R///acCG#Q+r111rn   c                      t        dt        z  t        dd      t        u sJ t        dt        z  t        dd      t         u sJ y )Nrb   r   r_   r`   rc   rI   rU   r   rm   rn   ro   test_basic3rw   {   s>    1a$***1a$+++rn   c                  &   t        dt        z  t        t        z  z   t        d      dk(  sJ t        dt        z  t        t        z  z   t        d      dt        z   k(  sJ t        dt        dz  z  t        t        dz  z  z   t        d      dt        dz  z
  k(  sJ t        t        t        dz         t        t              z
  t        t              dk(  sJ t        dt        dz  dz   z  t        dt        f      dt        z  t        d      z  d	z  k(  sJ y )
Nr^   r   rb      rh   rg   i   rd   	   )rI   rU   rV   r*   r   rG   r   rm   rn   ro   test_basic4r{      s    1qsAq!Q&&&1qsAq!QU***1a4!AG)#Q+sQqSy888a!etAw&2.!333Q1q\Aq":.!B$tAw,q.@@@rn   c            	      \   t        dd      \  } }}t        | |z        t        |       t        |      z
  z
  }|j                  | t              dk(  sJ ||z  j                  | t              dk(  sJ t        dd      \  }}|dz  |dz
  |dz   z  t        |dz         z  |dz  dz   dz  z  d|dz  dz   |dz   z  z  z   d|z  t	        ||z        z  |dz  dz  d	z
  t        |dz  |dz  z         z  z   |dz  dz   dz  z  z
  z  }t        ||t              t
        |d
z  z  |dz  dz   dz  z  k(  sJ y )Nza b cTr\   r   ztau xr^   rb   rg         ?rd   )r   r   rI   r   r1   r   )abcAtaurU   exprs          ro   test_logr      sm   g-GAq!AaCCFSVO$A771b>QE==B1$$$Wt,FC6C!GcAg&s1q5z136A:/AAQIa%H E VD3K/36!8c>3sAvdH D 3 1fqj1_%% &D q"CFCFQJ?!::::rn   c                      t        t        t        dz
  d      dz   t        dz   z  t        dd      t        dd      k(  sJ y )N   rd   r^   rg   r_   rb      )rI   r)   rU   r   rm   rn   ro   test_piecewiser      s:    )AE1%)AE2Ar3?8Ar?RRRrn   c                     dt        t              z  t        dt        z  dz
  t        t        dddt        z  dz
  dz  z  z
              z  dt        z  dz
  dk\  fddt        z  z
  t        t        dddt        z  dz
  dz  z  z
              z  df      z  } t        t        dz  dz  t        dk  ft        dz  dz
  df      }t        t        dz
  d	z  t        d
k  ft        dz
  d	z  t        dkD  ft        t        t        dz
              df      }t	        | t        d      dk(  sJ t	        |t        d      dk(  sJ t	        |t        d
      dk(  sJ y )Nr^      rb   r   Tr~   g      ?rz   re   ri   rd   )r*   rU   r+   r   rI   )func1func2func3s      ro   test_piecewise2r      sK   d1gIi!A#'3tA1Q37Q,4F/G+H!H!A#PQ'K !1Wc$q1acAg\>'9":;;TBD DEq!tAvqCx(1Q3;*=>EA{AF+q1uk1q5-ADQQRUDTVZC[\E1"""1"""2!###rn   c                       G d dt               } t         | t              t        t              t	         | t              t        t              k(  sJ y )Nc                       e Zd Zed        Zy)test_basic5.<locals>.myc                 H    |t         j                  u rt         j                  S y N)r   rl   rj   )clsargs     ro   evalztest_basic5.<locals>.my.eval   s    ajj uu !rn   N)__name__
__module____qualname__classmethodr   rm   rn   ro   myr      s    		 
	rn   r   )r   rI   rU   r   rH   )r   s    ro   test_basic5r      s8    X 
 A2%1q""5555rn   c                      t        t        t        z  t        t        z  z   t        d      t        t        z  dt        z  z   k(  sJ y Nr^   )rI   rU   rV   rW   rm   rn   ro   test_issue_3885r      s1    1qsAq!QqS1Q3Y...rn   c                  >   t        t        t              t        z  t        d      dk7  sJ t        t        t              t        z  t        d      j                         dk(  sJ t        t        t        dd      j                  t        t        dt        d      fk(  sJ y )Nr   rb   rf   r`   )rH   r6   rU   doitargsr   rm   rn   ro   
test_Limitr      su    Q1a A%%%Q1a %%'1,,,Aqd#((Q1fTl,CCCCrn   c                     t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        d	d      d	k(  sJ t        t        t              t        d	d      d
k(  sJ t        t        t        dt        z        z  dz  t        dd      t        dd      k(  sJ t        t        t        dz         t        t              z
  t        t              t        t        j                   t        d      dz        k(  sJ t        t        t        t                    t        t              dk(  sJ t        t        t        t                    t        t               dk(  sJ t        t        t        t                    t        t              dk(  sJ t        t        t        t                    t        t               dk(  sJ y )Nrg   r_   rc   rh   ri   r   rb   r^         rd   r~   )
rI   r&   rU   r   r   rM   r   Halfr1   r%   rm   rn   ro   
test_floorr      sQ   q1b#&",,,q1b#&",,,q1b#&",,,q1b#&",,,q1a%***q1a%+++q1a%***q1a%***q1a%***q1a%***q1c3'3...q1c3'3... 51:aAs+x1~===q3w%(*Ar2k166'1Q4PQ66RRRR tAwB'1,,,tAwRC(B...a!1b)Q...a!1rc*b000rn   c                     t        t        t        t                    t        dd      dk(  sJ t        t        t        t                    t        dd      dk(  sJ t        t        t	        t                    t        dd      dk(  sJ t        t        t	        t                    t        dd      dk(  sJ t        t        dt        t              z         t        dd      dk(  sJ t        t        dt        t              z         t        dd      dk(  sJ t        t        dt	        t              z         t        dd      dk(  sJ t        t        dt	        t              z         t        dd      dk(  sJ y )Nr   r_   rc   ri   re   r   )rI   r&   r6   rU   r2   rm   rn   ro   &test_floor_requires_robust_assumptionsr      s   s1v1c*a///s1v1c*b000s1v1c*a///s1v1c*a///q3q6z"Aq#.!333q3q6z"Aq#.!333q3q6z"Aq#.!333q3q6z"Aq#.!333rn   c                     t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        dd      dk(  sJ t        t        t              t        d	d      d
k(  sJ t        t        t              t        d	d      d	k(  sJ t        t        t        dt        z        z  dz  t        dd      t        dd      k(  sJ t        t        t        dz         t        t              z
  t        t              t        t        j                   t        d      dz        k(  sJ y )Nrg   r_   ri   rc   r   rb   r^   rd   r      r~   )rI   r%   rU   r   r   rM   r   r   rm   rn   ro   test_ceilingr      s   QC(B...QC(B...QC(A---QC(B...Q3'1,,,Q3'1,,,Q3'1,,,Q3'1,,,Q3'1,,,Q3'1,,,QS)S000QS)S000 71Q3<!1a-!Q???S!GAJ.26+qvvgqQRtTUv:VVVVrn   c                     t        t        t        t                    t        dd      dk(  sJ t        t        t        t                    t        dd      dk(  sJ t        t        t	        t                    t        dd      dk(  sJ t        t        t	        t                    t        dd      dk(  sJ t        t        dt        t              z         t        dd      dk(  sJ t        t        dt        t              z         t        dd      dk(  sJ t        t        dt	        t              z         t        dd      dk(  sJ t        t        dt	        t              z         t        dd      dk(  sJ y )Nr   r_   rb   rc   re   r   )rI   r%   r6   rU   r2   rm   rn   ro   (test_ceiling_requires_robust_assumptionsr      s   Q!Q,111Q!Q,111Q!Q,111Q!Q,111SV$aC0A555SV$aC0A555SV$aC0A555SV$aC0A555rn   c                     t        t        t              t        t              t	        dd      k(  sJ t        t        t              dt        z  z  t        t              t	        dd      k(  sJ t        t        t              dt        z  z  t        t               t	        dt              k(  sJ t        t        t              t        z  t        t              t	        dt              k(  sJ t        t        t        t                    t        dd      dk(  sJ t        t        t        t                    t        dd      dk(  sJ t        t        t        t                    t        dd      dk(  sJ t        t        t        dz        t        dd      dk(  sJ t        t        d        t        t        dt        z  dz         t        dd      dk(  sJ t        t        dt        z  dz         t        dd      dk(  sJ t        t        t        t        j                  z         t        dd      t        d      dz  k(  sJ t        t        dt        z        t        d      t	        dd      k(  sJ y )	Nr   rb   r_   rc   rf   r^   c                  @    t        t        t              t        dd      S Nr   rf   )rI   r'   rU   rm   rn   ro   <lambda>ztest_frac.<locals>.<lambda>  s    uT!WaD9 rn   rg   )rI   r'   rU   r   rM   r6   r2   rR   
ValueErrorr   r   rm   rn   ro   	test_fracr      s   a!R K1$5555a1Q3B';q!+<<<<a1Q3RC(K2,>>>>a!Q#{1b'9999c!fq!S)Q...c!fq!S)Q...c!fq!T*a///adQ4(A---
:9:bdQhAs+q000bdQhAs+q000a!&&j!1a.!A$q&888acAq![A%6666rn   c                     t        t        t        t              t        z        t        dd      dk(  sJ t        t        t        t              t        z        t        dd      dk(  sJ t        t        t	        t               t        z        t        dd      dk(  sJ t        t        t	        t               t        z        t        dd      dk(  sJ y )Nr   r_   rc   rg   )rI   r&   r6   rU   r7   rm   rn   ro   test_issue_14355r     s    s1vax!Q,111s1vax!Q,111Awqy!1a-333Awqy!1a-333rn   c                      t        dd      } t        t        |       t        d| z        z  | d      dk(  sJ t        t        |       t	        | dz         z   t	        |       z
  | t
              t        dz  k(  sJ y )NrU   Trealrb   r   r^   )r   rI   r1   r6   r*   r   r   rU   s    ro   	test_atanr     sk    sAaQqS!1a(A---a4A;&a0!R8BqD@@@rn   c            
         t        t        t              t        d      dk(  sJ t        t        t        t                    t        d      dk(  sJ t        t        t	        t                    t        d      dk(  sJ t        t        t        t        dz               t        d      t        d      k(  sJ t        t        t        t        z         t        t        t        z
        z
  dt        z  z  t        d      t        t              k(  sJ t        t        t        t              t        dz  z        t        t              dk(  sJ t        t        t        t        t              t        dz  z        t        t        t        dz         t        dz   dz  z        z  dz
  z  t        t              dk(  sJ t        t        t        t        dz
        dz  dz
        t        dd      t        k(  sJ t        t        t        t                    t        d      t        k(  sJ t        t        t        t        t                          t        d      t        k(  sJ t        dd      } t        t        t        |       dz         t        |       z  | t              dk(  sJ t        | t        d| z  t        z         t        t        d| z  z
        z
  z  dz  | d      dk(  sJ t        t	        |       t        |       z  | t        d	      d
k(  sJ y )Nr   rb   r^   rd   r_   rW   Tr}   rc   ri   )rI   absrU   r6   r2   r   rV   r   r   r   r   r   rW   s    ro   test_set_signsr     sP   QA!###SVa#q(((SVa#q(((SQZ!Q'3q6111 #a!e*s1q5z)AaC0!Q747BBB SVAqD[!1b)Q...CAq!t$SQUQUQJ)>%??!CDaLPQQQQ SQZ]Q&'As3r999 SVa#r)))SQ[!1a(B... 	sT"ASVaZQ'B/1444 C!aL3q1Q3w</02Aq9Q>>> QQB,222rn   c                  *   t        dd      } t        t        d| z        t        |       z   | dd      t	        dd      k(  sJ t        t        dt        t        |             t        t        d| z              z  z         | d      t        d      k(  sJ y )	NrU   Tr   rb   r   r_   ri   r^   )r   rO   r6   r1   rM   rI   r   r*   r   s    ro   test_heuristicr   8  s}    sAc!A#ha(!Q4B8JJJJQd1gtC!H~5561=QGGGrn   c                      t        dd      } d| z  t        |  t        z        z  }t        |t        t              dk(  sJ |j                  t        t              dk(  sJ y )NrW   Tr}   ri   r   )r   r   rU   rI   r   )rW   fs     ro   test_issue_3871r   >  sS    sT"A
1S!AYAAr?a771b>Qrn   c                  r   t        d      } t        dd      }t        d|| z  z   | z  | t              t        |      k(  sJ t        d|d| z  z  z   | z  | t              t        |dz        k(  sJ t        d|d| z  dz   z  z   | z  | t              t        |dz        k(  sJ t        |dz
  |dz   z  |z  |t              t        d      k(  sJ t        ddd|z  z   |z  z   |t              dt        j
                  z   k(  sJ t        dd|z  z   |z  d|z  |z  z  |t              t        t	        d	            k(  sJ y )
NrY   rU   Tr   rb   r^   rg   r   z1/3)r   rI   r   r   r   Exp1rY   rU   s     ro   test_exponentialr   E  s6   sAsA!ac'Aq"%Q///!a1g+!1b)S1X555!a1qk/A%q"-QqS9991q51q5/A%q"-R888a!A#g\!1b)QZ777!ac'AqsQh&2.#ah-???rn   c                      t        d      } t        dt        | t        |       z   z  z   | z  | t              t        t              k(  sJ y )NrY   rb   )r   rI   rU   r6   r   r   )rY   s    ro   test_exponential2r   P  s<    sA!aSVn$q(!R0CF:::rn   c                      t        dt        z  t              } t        | t        t              }|j	                         t        u sJ y r   rF   rU   rH   r   r   r   ls     ro   	test_doitr   U  s1    QAaBA668r>>rn   c            
         t        t        t              t        t        dz         z
  t        t              t	        dd      k(  sJ t        t        t              t        t        dz         z
  dz   t        t              t	        dd      k(  sJ t        t        t              t        t              t        t              z  z
  t        t              t	        dd      k(  sJ dt        d      z   dz  } dt        d      z   dz  }t        t	        | |      ddt        d      z   z  d      }t        t        t        t        t              j                  t              t        d	t        f      j                         j                  t                    t        t              |k(  sJ t        t	        dt        d      dz  z   t        d      dz  dz         ddt        d      z
  z        }t        t        t        t        t              j                  t              t        d	t        f      j                         j                  t                    t        t              |k(  sJ t        t        t              dz   dz  t        z  t        t              t	        d	t              k(  sJ dt         z  t        t              dz   t        z  z  }t        |t        t              t	        d	t              k(  sJ y )
Nrb   rg   r^   ri   rd   rh   F)evaluater   )rI   r6   rX   r   rM   r2   rN   rK   r   rY   rewriter   r   rU   )lohit1t2es        ro   test_series_AccumBoundsr   [  s   Q#a!e*$a,B0BBBBQ#a!e*$q(!R0KA4FFFF Q#a&Q-'B/;r13EEEE s1v+qB
c!f*aB	[R !R#a&[/E	BB#c!fnnS1Aq!9=BBDLLSQRTUWYZ^````	[c!fQhAq15q!c!f*~	FB#c!fnnS1Aq!9=BBDLLSQRTUWYZ^````3q6A:q.1$a,Ar0BBBB 	
QBQ!aAAr?k!R0000rn   c                  @   t        t        dt              t        t              dk(  sJ t        t        dt              t        t               dk(  sJ t        t        dt              t        t        t        z        t        t        z  k(  sJ t        t        dt              t        t         t        z        t         t        z  k(  sJ t        t        dt              t        t              dk(  sJ t        t        dt              t        t               dk(  sJ t        t        dt              t        t        t        z        t         k(  sJ t        t        dt              t        t         t        z        t         k(  sJ t        t        dt              t        t              t        k(  sJ t        t        dt              t        t               t         k(  sJ t        t        dt              t        t        t        z        dk(  sJ t        t        dt              t        t         t        z        dk(  sJ t        t        dt              t        t              dk(  sJ t        t        dt              t        t               t         t        z  k(  sJ t        t        dt              t        t        t        z        dk(  sJ t        t        dt              t        t         t        z        dk(  sJ t        t        dt              t        t              dk(  sJ y Nrb   r   )rI   r:   rU   r   r   r9   r8   r;   rm   rn   ro   !test_bessel_functions_at_infinityr   r  s9    A2&!+++AB3'1,,,A1R4(BqD000AA2b5)bSU222A2&!+++AB3'1,,,A1R4(RC///AA2b5)bS000A2&",,,AB3'B3...A1R4(A---AA2b5)Q...A2&!+++AB3'B3q5000A1R4(A---AA2b5)Q... A2&!+++rn   c                      t        dt        z  t              } t        | t        t              }|j	                  d      |k(  sJ y )Nr^   Fdeepr   r   s     ro   
test_doit2r     s8    QAaBA66u6"""rn   c                      t        t        t        t              z  t        t              dz
  z  t        t               dk(  sJ y r   rs   rm   rn   ro   test_issue_2929r     s0    !c!f*s1vz*As3q888rn   c                     t        dt        t              z
  t        dz  z  t        t        j                        ddt        t        j                        z  z
  k(  sJ t        t        t        t        dz         dz         t        d      t        dt        d      z         k(  sJ t        t        t        t        dz         dz         t        d      dt        d      z   k(  sJ y )Nrb   r^   r   r   )rI   r2   rU   r   r   r6   r   rm   rn   ro   test_issue_3792r     s    !c!f*ad"Aqvv.!aAFFm2CCCCSQZ!^$a+s1s1v:>>>SQZ!^$a+q3q6z999rn   c                     t        dt        dz   z  t        d      t        dd      k(  sJ t        dt        t        z   z  t        d      t        j
                  dt        z   z  k(  sJ t        t        t              t        dz  dz   z  t        d      t        d      dz  k(  sJ t        t        t              t        dz  t        z   z  t        d      t        d      dt        z   z  k(  sJ y )Nrb   rd   r^   re      r   )rI   rU   r   r   r   Oner   rm   rn   ro   test_issue_4090r     s    AEAq!Xa^333AFQ"aeeQVn444QA"Aq)SVAX555QA#Q*c!fa"fo===rn   c                      t        t        t              t        dd      t        u sJ t        t        t              t        t        dz  d      dk(  sJ y )Nr   r_   r`   r^   )rI   r3   rU   r   r   rm   rn   ro   test_issue_4547r     s@    QA3'2---QBqDc*a///rn   c                  x   t        t        dz  t        t              t        dz  cxk(  r	t        u sJ  J t        t        dz  t        d      dk(  sJ t        t        dz  t        d      dk(  sJ t        t        dz  t        t              dk(  sJ t        t        dz  t        d      t        j                  k(  sJ y )Nr~      r   r   g      )rI   rU   r   r   r   rm   rn   ro   test_issue_5164r     s    CB2s70b00000CB1$$$CA!###TAr"a'''TAq!QVV+++rn   c                  d    ddt         z  z   dt         z  z  } t        | t         d      t        k(  sJ y )N      ?r   )rU   rI   r
   )funcs    ro   test_issue_5383r     s0    cAg1-Dq!!!!rn   c                  F   t         t        d      dz  z   t        t               z  t         z
  t        dt        z        dz  z   t        t	        t                     z
  t        d      dt         z  z  z   t         dz  z  } t        | t         t              t        d      dz  k(  sJ y )Nrb   r^   r   rd   ih  )rU   r   r   r   r   rI   r   r   s    ro   test_issue_14793r     s    1aZ3q6!A%AbD	!3IaLaD"Q$K()*A.Dq"1c)))rn   c                     t        t        t        t         gddgddt        j                  t        dd      gddg            } g t        t        t         t        t         t        z  t        t         dt        dd      z  z  t        ddddddddt        t        t        t         t        t         t        z  t        t         dt        dd      z  z  dddddddd}t        |       t        |      k(  sJ t        t        | |            D ]0  \  }\  }}|\  }}}}|||z  z  }		 t        |	t        d|      |k(  sJ 2 y # t        $ r 	 J w xY w)	Nri   rb   r^   rd   rc   r_   r   r`   )listr   rU   r   r   r   r   r   len	enumerateziprI   AssertionErrorprint)
testsresultsir   resrV   sr   deqs
             ro   test_issue_5183r    s   !aRaQA7s% &E'r '2 's 'B 'A 'r 'B3Xa^/C+C 'R '''''''!"'$%''''3' "'%'CE'+-'02sB!Q3G/G' ' ' ' ' '  ' "#' %&'G u:W%%%#Cw$78 
;D#
1a1X	Qq)S000	

  	 t	s   EE)c                  D   t        t        t              t        z  t        t              dk(  sJ t        t	        t              t        t              t
        dz  k(  sJ t        t        t              t        t              t        u sJ t        t        t              t        z  t        t              dk(  sJ t        t        t              t        t        j                        t        t
              k(  sJ t        dd      } t        | t        d| z        z  | d      dk(  sJ y )Nr   r^   rTr   rb   )rI   r6   rU   r   r1   r   rC   r2   r   r   r*   r   r  s    ro   test_issue_5184r    s    Q1b!Q&&&a!R BqD(((q1b!R'''Q1b!Q&&&q1aff%b111sA3qs8Q"a'''rn   c                  t    t        dt        z   dt        z  z  t        j                  z
  t        d      dk(  sJ y r   )rI   rV   r   r   rm   rn   ro   test_issue_5229r
    s.    !a%1Q3!&&(!Q/1444rn   c                     t        t        t        t        gt         dz  dt        dz  t        t        t        dd      z  gddg            } ddt         t        ddt         t        ddt        t         ddt        t         ddt        t         f}t        |       t        |      k(  sJ t        t        | |            D ]3  \  }\  }}|\  }}} |t              }	 t        |t        ||      |k(  sJ 5 y # t        $ r 	 J w xY w)Nr^   r   rd   rc   r_   r`   )r   r   r3   r7   r   r   r   r   r   r   rU   rI   r   r   )	r   r   r   r   r   r   r   r  r  s	            ro   test_issue_4546r    s   #s#a%BqD"b!Q.?@s% &E !bS"aRCQB31b2#q!R"6Gu:W%%%#Cw$78 
;D#1aqT	Qq)S000	

  	 t	s   C44Dc                      t        dt        t        d      z  z   dt        z  z  t        d      dk(  sJ t        ddt        z  z  ddt        z  z  z   t        z  t        d      dk(  sJ y )Nrb   rd   r   re   )rI   rU   r   rm   rn   ro   test_issue_3934r    s_    !aQi-1Q3'A.!333!ac(Q1X%)1a0A555rn   c            	          t        t        t        dd      z  dt        t        dd      z  z   z  t        t              dk(  sJ t        t        dz  dt        dz  z   z  t        t              dk(  sJ y )NM   rd   rb   gfffffFY@)rI   rU   r   r   rm   rn   ro   test_calculate_seriesr    sc     HRO#QHRO);%;<aDIIIE1q%x<(!R0A555rn   c                     t        t        dz  dt        dz  z   z  t        t              dk(  sJ t        t        dz  dt        dz  z   z  t        t              dk(  sJ t        t        dz  dt        dz  z   z  t        t              dk(  sJ t        t        dz  t        dz   dz  t        t               z   z  t        t              dk(  sJ y )Nr   rb   d   i]    rI   rU   r   r   rm   rn   ro   test_issue_5955r  	  s    !R%!ae)$a,111!S&1q#v:&2.!333!T'A4K(!R0A555!T'AED=3r723a<AAArn   c                      t        t        dt        t              z        t        t	        t                    z  t        d      dk(  sJ y r   )rI   r   r6   rU   r3   rm   rn   ro   test_newissuer    s2    Qs1vXs3q6{*Aq1Q666rn   c                     t        t        t        z
  t        t              t        t        t        z
  t        t              k(  sJ t        dt        t	        t              z   z  t        z
  t        d      t        dt        t	        t              z   z  t        z
  t        d      k(  sJ t        t        t        z  t        t              t        t        t        z  t        t              k(  sJ t        t        t        z
  dt        z  z   t        t              t        t        t        z
  dt        z  z   t        t              k(  sJ y r   )rI   rU   r   rH   r6   rm   rn   ro   test_extended_real_liner    s    RB5RB#7777AAJ"$a+uQCF
^b5H!Q/OOOOAq"r!tQ!3333R!A#q"%q2v!|Q)CCCCrn   c                      t        dd      } t        |       t        z  t        d|       k7  sJ t        t        | dz  dz
  z  | t              t        u sJ y )NrU   Tr}   rb   r^   r   )r   rP   r   rI   r   s    ro   test_order_oor    sM    sT"A8B;%1+%%%QTAX2&",,,rn   c                  H    t        t        d        t        t        d        y )Nc                  T    t        t        t        t        z        t        t              S r   rI   r   rU   rV   r   rm   rn   ro   r   z!test_issue_5436.<locals>.<lambda>#  s    c!A#h2(> rn   c                  V    t        t        t         t        z        t        t              S r   r  rm   rn   ro   r   z!test_issue_5436.<locals>.<lambda>$  s    c1"Q$iB(? rn   rR   NotImplementedErrorrm   rn   ro   test_issue_5436r#  "  s    
 >?
 ?@rn   c                  H    t        t        d        t        t        d        y )Nc                  0    t        t        t        dd      S )Nr   r`   rH   rU   rm   rn   ro   r   z test_Limit_dir.<locals>.<lambda>(  s    eAq!3 rn   c                  0    t        t        t        dd      S )Nr   0r`   r&  rm   rn   ro   r   z test_Limit_dir.<locals>.<lambda>)  s    uQ1#6 rn   )rR   	TypeErrorr   rm   rn   ro   test_Limit_dirr*  '  s    
934
:67rn   c                      t        t        dz   dz  t        dz   dz  dz   z  t        t              dk(  sJ t        t        dz   dz  t        dz   dz  dz   z  t        t               dk(  sJ y )Nrb   r  rv   rm   rn   ro   test_polynomialr,  ,  sf    !a%$Q 12Ar:a???!a%$Q 12As;q@@@rn   c                     t        dt        z  dt        t        z   z  t        t        t        z   z  t        z  z   t        z  z
  t        t              t        dz
  t        t        z  z  k(  sJ t        dt        z  dt        t        z   z  t        t        t        z   z  t        z  z   t        z  z
  t        t               t        dz
  t        t        z  z  k(  sJ y Nrb   )rI   rV   rU   rW   r   rm   rn   ro   test_rationalr/  1  s    11q5	Aq1uIaK/22Ar:q1uqsmKKK11q5	Aq1uIaK/22As;A!}LLLrn   c                      t        t        t              t        z  t        dt        z        t        z  z
  t        d      t
        t        t        t        z
        z  k(  sJ y Nr^   r   )rI   r   rU   rW   rV   r   r   rm   rn   ro   test_issue_5740r2  6  s>    QC!HQJ&1-DQK???rn   c                      t        ddd      } | dz   t        | dz   z  z  t        | dz   z  dz
  z  t        t        dz
  z  z
  }t        |t        d      j                         | dz  k(  sJ y )NrY   TrZ   rb   r^   )r   rU   rI   cancel)rY   r  s     ro   test_issue_6366r5  :  sg    sD40A	
QAE
AAJN+aQi7AAq>  "ac)))rn   c                     t        t              } t        | t        t              t        u sJ t        t        | z  t        t              dk(  sJ t        | t	        dt
        z  t        z        t        t        z  t        z  z  z  t        t              dk(  sJ t        | t        t               t        t               k(  sJ y )Nr   r^   rb   )r   rU   rI   r   r*   r   r
   rC   r   s    ro   test_factorialr8  @  s    !AAr?b   1a!!! D2aL!A#)*Ar2a777AsubSz)))rn   c                     dt         dz  z  dz  t         t        dd      z  z
  t        dt         dz  z  dz  t        j                  z
  z  dt         dz  z  dz  z   dt         dz  z  dz  z
  t        dd      z   dt        dz   z  z  z   } t        | t        t              dt         dz  z  dz  dt         dz  z  dz  z   dt         z  dz  z
  t        dd      z
  k(  sJ y )	Nre   rd   r   r^   #   ry      rb   )rU   r   rV   r   r   rI   r   r   s    ro   test_issue_6560r=  J  s    	
1a4Ahq!n$	$1QT6!8aff+<(=1WQY)')+AqD)35=a^)DFGQi(Q 
QAAr?a1fQh1a41AaCE9HQNJJJJrn   c                  X   t        d      t        dd      } t        d      }t        dd      }t        dd      }d	z  | z
  d
z   z  | | z
  d
z   z  z   z  |z  | d
z
  | z
  d	z   z  | | z
  d
z   z  z   z  |z  z  z   z
  |z  z
  z  j                  ||d
z         t        t        fd       t	        j                  ||      t
              d
k(  sJ t	        j                  ||      t
              j                         d	|d
z   z  | z   d
z
  | d
z   |d
z   z  z  k(  sJ y )NrY   r  Tr}   r   pmnegativer^   rb   c                  &    t         t              S r   )rI   r   )r   rY   s   ro   r   z!test_issue_5172.<locals>.<lambda>Y  s    dAr(: rn   )r   subsrR   r"  rI   r   rK   )r  r   r?  r@  r   rY   s       @@ro   test_issue_5172rE  O  sO   sAsT"AsAsT"AsT"AqS!a%!)_a!QUQY-/014UQA	]A1q519$56::;=>?ABAKD99QAD
 :;1a!R(A---1a!R(113	
QUa!	a!eq1u--. . .rn   c                  |    t        d      } t        t        t        t        | z   z        t        t              dk(  sJ y )Nr   rb   )r   rI   r*   rU   r   r   s    ro   test_issue_7088rH  _  s.    sAaQi!R(A---rn   c                     t        t        t        t        z  dz         t        d      t        t        d      z
  k(  sJ t        t        t        t        z  dz         t        dd      t        d      k(  sJ t        t        t        t        z  dz
        t        d      t        d       k(  sJ t        t        t        t        z  dz
        t        dd      t         t        d      z   k(  sJ t        t        t        t        z  dz         t        d      t        d       k(  sJ t        t        t        t        z  dz         t        dd      t        d      k(  sJ t        t        t        t        z  dz
        t        d      t        d      k(  sJ t        t        t        t        z  dz
        t        dd      dt        z  t        d      z
  k(  sJ t        t        t        dt        z  z         t        d      t        t        d      z  k(  sJ t        t        t        dt        z  z         t        dd      t         t        t        d      z  z   k(  sJ t        t        t        dt        z  z
        t        d      t        t        t        d      z  z
  k(  sJ t        t        t        dt        z  z
        t        dd      t         t        d      z  k(  sJ t        t        dt        z        t        d      t        dz  k(  sJ t        t        dt        z        t        dd      t         dz  k(  sJ t        t        t              t        t              t        dz  k(  sJ t        t        t              t        t               t         dz  k(  sJ t        t        t        t        d      dz  t        z  z         t        d      t        t        t        t        d      dz        z  z
  k(  sJ t        t        t        t        d      dz  t        z  z         t        dd      t         t        t        d      dz        z  k(  sJ t        t        t        t        d      dz  t        z  z
        t        d      t        t        t        d      dz        z  k(  sJ t        t        t        t        d      dz  t        z  z
        t        dd      t         t        t        t        d      dz        z  z   k(  sJ t        t        t              t        d      t        dz  k(  sJ t        t        t              t        dd      t         dz  k(  sJ t        t        t        t        z  t        d      dz  z         t        d      t        t        d      dz        k(  sJ t        t        t        t        z  t        d      dz  z         t        dd      t        t        d      dz         k(  sJ t        t        t        t        z  t        d      dz  z
        t        d      dt        z  t        t        d       dz        z
  k(  sJ t        t        t        t        z  t        d      dz  z
        t        dd      t        t        d       dz        k(  sJ t        t        t        t        z  t        d      dz  z         t        d      t        t        d      dz        k(  sJ t        t        t        t        z  t        d      dz  z         t        dd      t        t        t        d      dz        z
  k(  sJ t        t        t        t        z  t        d      dz  z
        t        d      t         t        t        d      dz        z   k(  sJ t        t        t        t        z  t        d      dz  z
        t        dd      t        t        d      dz         k(  sJ t        t        t        t        z  dz
        t        d      t        t        z  k(  sJ t        t        t        t        z  dz
        t        dd      t         t        z  k(  sJ t        t        t         t        z  dz
        t        d      t         t        z  k(  sJ t        t        t         t        z  dz
        t        dd      t        t        z  k(  sJ t        t        t        t        z  dz
        t        d      t        k(  sJ t        t        t        t        z  dz
        t        dd      t         k(  sJ t        t        t         t        z  dz
        t        d      t         k(  sJ t        t        t         t        z  dz
        t        dd      t        k(  sJ t        t!        t        t        z  dz
        t        d      dt        d      dz  z  k(  sJ t        t!        t        t        z  dz
        t        dd      dt        d      dz  z   k(  sJ t        t!        t         t        z  dz
        t        d      dt        d      dz  z   k(  sJ t        t!        t         t        z  dz
        t        dd      dt        d      dz  z  k(  sJ y )Nr^   r   rc   rg   rb   ri   rd   )rI   r0   r   rU   r   r,   r1   r   r   r-   r   r    r/   r.   r   r*   r(   rm   rn   ro   test_branch_cutsrJ  d  s   acAg1%d1g555acAg1c*d1g555acAg1%$q'111acAg1c*rcDGm;;;acAg1%$q'111acAg1c*d1g555acAg1%b111acAg1c*adT"Xo===a!A#g1%58333a!A#g1c*rcAeAhJ.>>>>a!A#g1%aaj888a!A#g1c*qbqk999acAq!RT)))acAq#&2#a%///a!R BqD(((a!bS!bSU***a!A$q&(l#Q*b1U1Q46]?.BBBBa!A$q&(l#Q3/A2eAaDFm3CCCCa!A$q&(l#Q*aad1fo===a!A$q&(l#Q3/B351a=3HHHHa!Q2a4'''a!Q$A---acAaDFl#Q*d1Q46l:::acAaDFl#Q3/D1aL=@@@acAaDFl#Q*adT1Q4%'].BBBBacAaDFl#Q3/41a=@@@acAaDFl#Q*d1Q46l:::acAaDFl#Q3/2QqT!V3DDDDacAaDFl#Q*rcD1aL.@@@@acAaDFl#Q3/D1aL=@@@QqS1Wq!$",,,QqS1Wq!S)aRU222aRTAX1%!B...aRTAX1c*ad222acAg1%***acAg1c*qb000qbdQhA&1",,,qbdQhAs+q000acAg1%"!Q777acAg1c*ad1f~o===qbdQhA&B!A$q&>/999qbdQhAs+ad1f~===rn   c                      t        d      } t        dt        dt        z         t        |       dz  z  z
  t        dt        z
        t	        |       dz  z  z
  z  }t        |t        d      dt	        |       dz  t        j                  z
  z  k(  sJ y )Nr   rb   r^   r   )r   rW   r*   r6   r2   rI   r   r   )r   r   s     ro   test_issue_6364rL    su    sA	1tAE{3q619$$tAE{3q619'<<=AAq>QA	AFF 23333rn   c                      t        t        dt        t               z        t        dz  z  t        d      t        dt        z        k(  sJ y r1  )rI   r   r<   rU   r   rm   rn   ro   test_issue_6682rN    s9    Qr1"vXq!t#Q*c!J,.????rn   c                     t        d      } t        | t        z  t        d      t        t	        |       z  k(  sJ t        |  t        z  t        d      t         t	        |       z  k(  sJ t        |  t        z  t        t              t         t	        |       z  k(  sJ t        | t        z  t        t              t        t	        |       z  k(  sJ y )Nr   r   )r   rI   rU   r   r   rG  s    ro   test_issue_4099rP    s    sA1ar$q'z)))!Aq!DG+++!Aq""T!W,,,1a47
***rn   c            	         t        d      } t        t        dt        t        | z         z         t        dt        t              z         z
  | z  | d      t        t              dt        t        t              dz         z  z  k(  sJ y )Ndxrb   r   r^   )r   rI   r*   r   rU   )rR  s    ro   test_issue_4503rS    sl    	B$q3q2v;'$q3q6z*::B>AFA$s1vz""#$ $ $rn   c                      t        ddddt               } t        |       }t        |t        dd      dk(  sJ t        |t        t              t         k(  sJ y )Nrm   )rb   )r   r   rf   )rE   rU   rL   rI   r   )Ggs     ro   test_issue_6052rW    sP    BdQB'AAAAq$1$$$Ar?rc!!!rn   c                  D   t        t              t        dt        dt        z              z  } t        t        t	        | t        t              z  | z  t        d      dk(  sJ t        t        t	        | t        t              z  | z  t        d      j                         dk(  sJ y )Nrb   ry   r   r^   g       @)r*   rU   r8   rI   r   evalfr   s    ro   test_issue_7224rZ    s|    771T!A#Y''D4a##D(!Q/14444a##D(!Q/5573>>>rn   c                  `    t        t        t        dd      dz
  z  t        t              dk(  sJ y )Nrb   g    eAr   )rI   rY   r   r   rm   rn   ro   test_issue_8208r\    s*    Xa%)*Ar2a777rn   c                      t        t        t        dd      z  dz
  t        t              dz
  t        dd      z  z  t        d      dk(  sJ y )Nrb   r   r^   rd   r   r   )rI   rU   r   r*   rm   rn   ro   test_issue_8229r^    sB    !Xa^#a'$q'A+A)FF2NRSSSSrn   c                  n    t        dd      \  } }t        t        d|| z  z
        |t              dk(  sJ y )Nzd tTr}   rb   ri   )r   rI   r=   r   )r  ts     ro   test_issue_8433ra    s5    54(DAqQ1Wq"%+++rn   c                      t        ddd      } t        dd      }t        || z  t        |       z  t        |       z  | t              dk(  sJ y )NrX   T)r[   nonnegativelamdar}   r   )r   rI   r   r   r   )rX   rd  s     ro   test_issue_8481re    sK    sDd3A7T*ECK')A,62>!CCCrn   c                      t        t        t        t        dz        t        t              t        k(  sJ t        t        t        t        dz        dt         z  z  t        t              dk(  sJ y )Nr^   rd   r   )rI   r   rY   r   rm   rn   ro   test_issue_8462rg    sQ    !QqS!1b)R///!QqS!A1"I-q"5:::rn   c                      t        ddd      } t        d      }t        || z  |t               t        t        d| z        z  k(  sJ y )NrY   TrZ   rU   ri   )r   rI   r   r   r   s     ro   test_issue_8634ri    sC    sD40AsAAq2#"T2']"2222rn   c                  z   t        dd      } t        dd      }t        | t        z  | t        dz
  z  z
  | t              dk(  sJ t        | t        z  | t        dz
  z  z
  | t              t        k(  sJ t        | t        z  | t        dz
  z  z
  | t              t        k(  sJ t        | t        z  | t        |z
  d	z
  z  z
  | t              t        k(  sJ t        dd      } t        | t        z  | t        d	z
  z  z
  | t              t        k(  sJ t        | t        z  | t        d
z   z  z
  | t              t         k(  sJ y )NrU   Tr   rX   r}   r   re   g      @rb   r^   )r   rI   rY   r   )rU   rX   s     ro   test_issue_8635_18176rk    s   sAsT"AAAE
"Ar*a///AAE
"Ar*b000AAG$a,222AAEAI&2."444sT"AAAE
"Ar*b000AAE
"Ar*rc111rn   c                  X    t        t        t              t        t              t        u sJ y r   )rI   r   rU   r   rm   rn   ro   test_issue_8730rm    s    a!R(B...rn   c                       t        dd      t        dd       t        t              t              z  z  d z   z  z  t              dk(  sJ t	        t
         fd       y )	NrY   Tr[   r   r}   rb   r   c                  b    t        t              t              z  z   z  z  t              S r   )rI   r   r   r   rY   s   ro   r   z!test_issue_9252.<locals>.<lambda>  s*    s1v3q6.BQT.I1b(Q rn   )r   rI   r   r   rR   r"  rq  s   @@ro   test_issue_9252rr    s\    sD!AsT"A#a&Ac!fH%Q
2Ar:a???
 QRrn   c                  R    t        t        t              dz  t        dd      dk(  sJ y )Nr;  r   rc   )rI   r6   rU   rm   rn   ro   test_issue_9558rt    s#    QQ3'1,,,rn   c                      t        dt        z  t        t        dt        z  t              dz  z  z  t        t              t        k(  sJ y )Nr   r^   )rI   rX   r   r   r   rm   rn   ro   test_issue_10801rv    s7    Q!hqsA.112Ar:b@@@rn   c                  x    t        dd      \  } }t        t        | |z        t        |       z  | d      |k(  sJ y )Nzs xTr   r   )r   rI   r=   )r  rU   s     ro   test_issue_10976rx    s9    5t$DAqQqS#a&!Q'1,,,rn   c                      t        t        t              t        t        d      z  t        z  t	        dt
        z  t        z        z  z  t        t              dk(  sJ y Nrb   r^   )rI   r   rY   r   r*   r   r   rm   rn   ro   test_issue_9041r{    s?    1!CF(Qad1f!=>2F!KKKrn   c                  .   t        d      \  } }}t        | | |      j                  |hk(  sJ t        | | |d      j                  |hk(  sJ t        | |z   | |z   |      j                  |hk(  sJ t        | dz   |z   | dz  |      j                  ||hk(  sJ y )Nzx, y, arc   r^   )r   rH   free_symbols)rU   rV   r   s      ro   test_issue_9205r~    s    i GAq!Aq>&&1#---Aq#++s222QAq!..1#555!Q$AqD!$11aV;;;rn   c                      t        dt        t        d      z  t        dz  z  t        t              dk(  sJ t        dt        t        d      dz   z  t        dz  z  t        t              dk(  sJ y )N   rd   rb   )rI   r   rY   r   rm   rn   ro   test_issue_9471r  	  s[    2Aa>1a4'2.!3332Aa
#QT)1R0B666rn   c                      t        t        t        dz         t        t              z  t        t              t        k(  sJ y r.  )rI   r   rY   r   r   rm   rn   ro   test_issue_10382r    s+    1q5!)A,.26+EEErn   c                  j    t        t        t        dt        z              t        t              dk(  sJ y rz  )rI   r>   r   rU   r   rm   rn   ro   test_issue_11496r    s%    c!A#hB'1,,,rn   c                      t        t        t        t        z   t        z  t        t        z  z
  t        z  t        d            t        t        t        dz
  z  z  k(  sJ y Nr   rb   )rK   rI   rU   rV   rY   rm   rn   ro   test_issue_11879r    s?    EAaC!8AqD=!+Q23qQqSzAAArn   c                      t        d      } t        d| z  | t              dk(  sJ t        dd| z  z  | t              t        dd      k(  sJ y )NrX   r   rb   g333333?rd   
   )r   rI   r   r   )rX   s    ro   test_limit_with_Floatr    sK    A1b!Q&&&S!VQ#x2666rn   c                      t        dt        z  dt         dz
  z  z  t        dz   dz  z  t        dz  z  t        t              t        dd      k(  sJ y Nrd   rb   r^   )rI   rU   r   r   rm   rn   ro   test_issue_10610r     sH    Aa1"q&k!1q51*,QT11b9Xa^KKKrn   c                  6   t        t        t              t        t              z   t        dd      t        d      k(  sJ t        t        t              t        t              z   t        dd      t        d      dt        z  t
        z  z   k(  sJ t        t        d        t        t        t              t        t              z   t        t              t        k(  sJ t        t        t              t        t              z   t        dd      t        d      k(  sJ t        t        t              t        t              z   t        dd      t         k(  sJ t        t        d        t        t        t              t        t              z   t        t              t        k(  sJ y )Nr   r_   r^   rc   c                  `    t        t        t              t        t              z   t        dd      S r   )rI   r   rU   r"   rm   rn   ro   r   z"test_issue_10868.<locals>.<lambda>'      uSVeAh%61dC rn   c                  `    t        t        t              t        t              z   t        dd      S r   )rI   r   rU   r!   rm   rn   ro   r   z"test_issue_10868.<locals>.<lambda>+  r  rn   )
rI   r   rU   r"   r   r   rR   r   r   r!   rm   rn   ro   test_issue_10868r  $  s   Q%("Aq#.#a&888Q%("Aq#.#a&1Q3r6/AAA
:CDQ%("Ar*b000Q%("Aq#.#a&888Q%("Aq#.2#555
:CDQ%("Ar*b000rn   c                  n    t        t        t        t              z   t        z  t        t              dk(  sJ y r.  )rI   rY   r2   r   rm   rn   ro   test_issue_6599r  /  s%    !c!f*aB'1,,,rn   c                  ,   t        dt        z  dt        dz  z  z   t        dz  t        t              z   z  t        t               dk(  sJ t        dt        z  dt        dz  z  z   t        dz  t        t              z   z  t        t              t        u sJ y )Nrd   r^   r  rs   rm   rn   ro   test_issue_12555r  3  st    !Q$ArE/aec!fn5q2#>!CCC!Q$ArE/aec!fn5q"=CCCrn   c                     t        dd      \  } }}t        ddd      \  }}}}}}}	||z  ||z  z  | z  |z  t        |dz  |d|z  z  z  |dz  z  |dz
  z  |d|z  z  |dz  z  |dz  z  |dz
  z  z   |d|z  z  |d|z  z  z  |dz  z  |dz
  z  |dz  d|z  z
  dz   z  z   d|d|z  z  z  ||dz   z  z  |z  | z  |z  |dz  d|z  z
  dz   z  z
  d||dz   z  z  |d|z  z  z  |z  | z  |z  |dz  d|z  z
  dz   z  z   d||dz   z  z  ||dz   z  z  |dz  z  |dz
  z  z
  |dz
  |dz  d|z  z
  dz   z  z        z
  || z  |z
  | z
  dz   z  }
|
j                  ||      j                  d      t	        |
||      j                  d      k(  sJ y )	Nzr z xTr   za b s0 K F0 s T)r\   r   r^   rb   r   )r   r*   rD  factorrI   )r  rW   rU   r   r   s0KF0r  Tfxs              ro   test_issue_12769r  8  s3   gD)GAq!#$54PAq"aQ
a%1*Q,r/D"a%AaC.A"5q1u"=
QqS	!Q$q!tQU##$&(1Q3iAaC&8Q&>A&F1qQRs
UV&W#X	"qs)AAJq "2%q!taczQ7#8 	
"q1u+a!A#hq "2%q!taczA~6#7 	
"q1u+a!a%j A%q1u-	#. 23QA!a0H	"J K K NOqSTUXXY\\]M]	
_B 771b>  d +uRB/?/F/FD/F/QQQQrn   c                  L   t        t        d      ddt        z  dz
  z  z  dt        z  t        z  z  dt        z  dz   dt        z  dt        j                  z  z   z  z  dt        z  dz   dt        z  dt        j                  z  z
  z  z  t        t
              t        d	d
      k(  sJ y )N   re   rb   i@  r^   r   i   $   )rI   r*   rU   r   r   r   r   rm   rn   ro   test_issue_13332r  D  s    b!bdQh-'q14acAg1qx5PP1qBqD1QVV8O,-./58@R8HI I Irn   c                  F   t        t        dz  t        t        t              z  z   t        t              z   t        t               t        u sJ t        t        dz  t        t        t              z  z   t        t              z   t        t              t        u sJ t        t        t        t              z   dz  j                         t        t              t        u sJ t        t        t        t              z   dz  j                         t        t              t        u sJ t        t        t        t              z   dz  j                         t        t               t        u sJ t        t        t        t              z   dz  j                         t        t               t        u sJ y r   )rI   rU   r6   r2   r   expandrm   rn   ro   test_issue_12564r  I  s   A#a&3q6)1rc2b888A#a&3q6)1b1R7771s1v:/))+Q3r9991s1v:/))+Q3r9991s1v:/))+Q4:::1s1v:/))+Q4:::rn   c                  H    t        t        d        t        t        d        y )Nc                  b    t        t        t              t        t              j	                         S r   )rH   r   rU   r   r   rm   rn   ro   r   z"test_issue_14456.<locals>.<lambda>S  s    c!fa(=(B(B(D rn   c                  j    t        t        dz  t        dz   z  t        t              j                         S )Nr^   rb   )rH   rU   r   r   rm   rn   ro   r   z"test_issue_14456.<locals>.<lambda>T  s$    adAaCj!S(A(F(F(H rn   r!  rm   rn   ro   test_issue_14456r  R  s    
 DE
 HIrn   c                      t        dt        dt        z  t        z  t        dz  z
        z  t        dt        z  dt        z  dz
  z        t         u sJ y )Nrd   r      r^   )rI   r5   r   rU   r   rm   rn   ro   test_issue_14411r  W  sF    3qtAv!|$$a2r"uqy)9:rcAAArn   c                      t        t        t        dz   dz  dz   t        dz  dz   z  dz
  z  t        t              dk(  sJ y rz  rv   rm   rn   ro   test_issue_13382r  [  s<    a!eaZ!^adQh/!34a<AAArn   c            	          t        t        dt        t        t        dz         z   dz   t        t        t              z   z  z   z  t        t              dk(  sJ y )Nri   rb   rI   rU   r   r   rm   rn   ro   test_issue_13403r  _  sA    B!c!a%j.1,q3q6z::;QCqHHHrn   c                     t        t        dz   t        t              dz  z  t        dz
  t        dz   dz  z  t        t        dz         dz  z  z   t        dz  t        t              dz  z  z  t        t              dk(  sJ y r  r  rm   rn   ro   test_issue_13416r  c  sl    1a4%A	/QUQUQJ$6s1q5z1}$DDq!tCPQFTUI~VXY[]^bccccrn   c                     t        t        dz  dt        z  dddt        z  z  z
  t        z   dz   z  t        z
  t        dz   dz  t        dz  z   t        z  z
  z  t        t              t        dz  dz  t        dz  dz  z
  t        dz  z   k(  sJ y )Nr^   rb   r   rd   r  ry   r   )rI   rY   rU   r   rm   rn   ro   test_issue_13462r  g  s    Aqsa!QqS'kA--12Q61a4%'AaC-9JJKQPRSWXZ[W[\^W^abdeaefgagWgjklnjnWnnnnrn   c                      t        d      } t        t        | t        z
        t        t              dk(  sJ t        t        t        t              t        z
        t        t              dk(  sJ y )Nr   ri   )r   rI   r=   rU   r   r*   rG  s    ro   test_issue_13750r  k  sN    sAQUQ#r)))T!Wq[!1b)R///rn   c                  ,   t        t        t        t              t	        t              z  t        t
              t              sJ t        t        t        t              t        t              z  t        t
              t              sJ t        t        t        t	        t        t                          t        t
              t              sJ t        ddt        dz  t        t              z   z  z   t        dz  t        z   z  t        t
              t        k(  sJ y rz  )	
isinstancerI   r6   rU   r   r   rH   r2   r
   rm   rn   ro   test_issue_14276r  q  s    eCFCFNAr2E:::eCFCFNAr2E:::eCCF,a4e<<<!aAA''1a4!84a<AAArn   c                      t        dt        t              t        t              z  z  dt        z  z  t        t              dk(  sJ y r.  )rI   r   rU   r   rm   rn   ro   test_issue_14514r  x  s3    !SVSV^$!,a4999rn   c                     t        t        t              dz  t        t              z
  t	        t              t        t              z  z   t        t              t        t        j                  t        j                        k(  sJ t        t        t              dz  t        t              z
  t        t              t        t              z  z   t        t              t        t        j                  t        j                        k(  sJ t        t        t              t	        t              dz  z
  t        t              t        t        j                  t        j                        k(  sJ t        t        t              t	        t              dz  z
  t        t              t        t        j                  t        j                        k(  sJ t        t        t              t	        t              dz  z
  t        t              t        t        j                  t        j                        k(  sJ t        t        t              dz  t	        t              dz  z
  t        t              t        t        j                  t        j                        k(  sJ t        t	        t              dz  t        t              dz  z   t        t              z
  t        t              t        t        j                   t        j                        k(  sJ y r   )rI   r6   rU   r2   r7   r4   r   rM   r   rk   rl   r3   r   rm   rn   ro   test_issues_14525r  |  s   QSV#c!fSVm3Q;{1K]K]_`_i_i?jjjjQSV#c!fSVm3Q;{1K]K]_`_i_i?jjjjQ#a&!)#Q+{1;M;Mqzz/ZZZZQ#a&!)#Q+{1;M;Mquu/UUUUQ#a&!)#Q+{1;M;Mquu/UUUUQSVQY&2.+a>P>PRSRWRW2XXXXQSVQY&Q/B7;vqzz;ZZZZrn   c                      t        t        t              t        t        t        dz  z
        z  t        dz   z  t        t              dk(  sJ y )Nr^   rb   r   )rI   r*   rU   r2   r   rm   rn   ro   test_issue_14574r    s7    aQAX&!a%0!R8A===rn   c                  p   t        t        t              t        t              t        j
                  k(  sJ t        dt        t              z   t        t              dt        j
                  z   k(  sJ t        dt        t              z  t        t              t        dd      k(  sJ t        t        t              t        t              t        j
                  k(  sJ t        t        t              t        t               t        dd      k(  sJ t        dt        t              z  t        t               dk(  sJ y )Nrd   re   r^   ri   r   rg   )rI   rA   rU   r   r   r   r   r@   rm   rn   ro   test_issue_10102r    s    !a$...Xa[!R(AJ6668A;2&(1a.888!a$...!a"%"a8888A;B3'2---rn   c                  &    t        t        d        y )Nc                      t        t        t        t        z        t	        t
        t        z        z  t        t              S r   )rI   r   r   rU   r6   r   r   rm   rn   ro   r   z"test_issue_14377.<locals>.<lambda>  s$    c!A#hs2a4y.@!R(H rn   r!  rm   rn   ro   test_issue_14377r    s    
 HIrn   c                  ^   t         dz  dt         dz  z  dt         dz  dz
  z  t         dz  z  t        t         dz  dz         z  z
  dt         dz  dz
  z  t         dz  z  t        t         dz  t         z   dz         z  z   t         z   dz   z  } t        | t         t              t	        d      dz  k(  sJ y )Nr^   rg   rd   rb   )rU   rB   rI   r   r   r<  s    ro   test_issue_15146r    s    	
1AqD1adQh<!Q$.A1BBB	1a4!8q!tgadQhl334678:;< 	=AAr?ad1f$$$rn   c                     dt         z  ddt          z  ddt         z  z  t         z   dz   z  z   z  t         dz   z  t         dz   z  } t        | t         t              t        d      k(  sJ t	        t         d      dz  dt         z  t        t               z  z   dt         z  z   t        t         dz         dt        t               z  z   dt         z  z   z  } t        | t         t              dk(  sJ y )Nr^   rg   rb   r   r  re   rd   )rU   rI   r   r   r   r   r<  s    ro   test_issue_15202r    s    	
Aq1r7Bq!tGaK!O,,	-q1u	5Q?AAr?c!f$$$	QA1Yq\)	)AqD	0Yq1u5E)TU,5VY[]^Y^5^_AAr?b   rn   c                  t    t        t        dz  t        dz   dz  z
  t        dz  z  t        t              dk(  sJ y )Ni  rb   i  i0rv   rm   rn   ro   test_issue_15282r    s3    !T'QUTM)QW4a<EEErn   c                      t        t         t        t        t              dz         z   t        z  t        t        d      dk(  sJ y )Nrb   rc   r`   r   )rI   rU   r   r   r   rm   rn   ro   test_issue_15984r    s3    1"s3q6A:&)1bc:a???rn   c                  t    t        t        t        d      t        t              z  t        t              dk(  sJ y r.  )rI   rD   rU   rC   r   rm   rn   ro   test_issue_13571r    s)    Aq!E!H,a4999rn   c                      t        t        t        t                    t        d      t        t        t        j
                              k(  sJ y r.  )rI   r,   r?   rU   r   r   rm   rn   ro   test_issue_13575r    s.    d1g1%d155k)::::rn   c                     t        t        t              t        z  t        dd      j                         dk(  sJ t        t        dz  t        dd      j                         dk(  sJ t        dt        dz  z  t        dd      j                         t        u sJ t        dt        z  t        dd      j                         t
        u sJ y )Nr   rf   r`   rb   r^   )rH   r6   rU   r   r   r   rm   rn   ro   test_issue_17325r    s    Q1aT*//1Q666Aq!&++-2221a4A4(--/25551a%**,333rn   c                  T    t        t              j                  t        d      dk(  sJ y )Nr   )r   rU   rI   rm   rn   ro   test_issue_10978r    s!    A;Q"a'''rn   c                  ^    t        t        t        dz        t        t              t        u sJ y r   )rI   r&   rY   r   rm   rn   ro   test_issue_14313_commentr    s!    qsQ#r)))rn   c                      ddt         z  z
  t         z  j                  t               } t        | t         dd      dk(  sJ y )Nrb   r_   r`   )rU   r   rI   )r  s    ro   test_issue_15323r    s7    
ac'AAAAqc"a'''rn   c                      t        t        t        t                      t        t              z  t        d      dk(  sJ y r.  )rI   r   r   rU   rm   rn   ro   test_issue_12571r    s0    (CF7##CF*Aq1Q666rn   c                      t        t        dz  t        dz   t        z  t        z  z  t        dz   t        dz   z  t        dz   z  z  t        t              t        d      k(  sJ y r  r  rm   rn   ro   test_issue_14590r    sM    !Q$Q	A~%QQQ(?@!RHCPQFRRRrn   c                      t        d      \  } }t        t        |z  t        |z  z
  t        | z  t        | z  z
  z  t        t              |t        |  |z   z  z  | z  k(  sJ y )Na b)r   rI   rU   rV   r   r   s     ro   test_issue_14393r    sU    5>DAq!Q$A+1q!t,a3qaR!V}QFFFrn   c                      t        t        t        dz         dt        dz   z  z  t        t              dt        z  z  z
  t        t              t	        d      k(  sJ y )Nrb   ri   )rI   r   rY   r   r   rm   rn   ro   test_issue_14556r    sH    1q5!Aq1uI.1!1DDaLPSTVPWWWWrn   c                      t        dt        d      dz  t        dz   z  z   dt        z  z  dt        d      dz  t        dz
  z  z  z  t        t              t        k(  sJ y )Nrb   r^   rd   r   rI   r   rU   r   rm   rn   ro   test_issue_14811r    sU    11a1q5)*ad3a1Q46QU:K6LMqRTUY[[[[rn   c                  \    t        t        t              t        d      t        d      k(  sJ y )Ni ʚ;)rI   r   rU   rm   rn   ro   test_issue_16222r    s!    QJ'3z?:::rn   c                      t        t        t        dz   z  t        dz   t        z  z   t        t        dz   z  z  t        z  t        t              t        t        d            k(  sJ y r.  r  rm   rn   ro   test_issue_16714r    sI    1q1u:Q
*a!a%j81<aDCPQFSSSrn   c                  ^   t        dd      } t        t        t        | z   t              t        |  z  z  t        t              dt        | dz         z  k(  sJ t        ddd      } t        t        t        | z   t              t        |  z  z  t        t              dt        | dz         z  k(  sJ y )NrW   Tr}   rb   )r\   r[   )r   rI   r   rY   r   rC   r   s    ro   test_issue_16722r    s    d#A!a%#ArE)1b1QuQU|^CCCdD1A!a%#ArE)1b1QuQU|^CCCrn   c                      t        t        dz   dz   t        dz   dz   t        t        dz         z  z  t        dz   z  t        t              z  t        dz   z  t        t              dk(  sJ t        t        dz   dz  t        t              z  t        dz   t        dz   z  t        t        dz         z  z  t        t              dk(  sJ t        t        dz   t        t              z  t        t        t        dz         z  z  t        t              dk(  sJ y )Nrb   r^   r   rd   )rI   rY   r   r   rm   rn   ro   test_issue_17431r    s    1q5A+AEQ;)AE2B"BCa%$Q<(+,q5234b:=>? ? ?!a%!IaL(1q51q5/)AE:J*JKb  !a%9Q<'1yQ/?+?@!RHAMMMrn   c                      t        t        t        t                     t        t        t                    t        z  z
  t        d      t        k(  sJ y r.  )rI   r<   r   rU   r   rm   rn   ro   test_issue_17671r    s4    SVGs3q6{1},a3zAAArn   c                      t        dd      \  } }}}t        | dz   |z  t        | dz   dz  |dz  z  ||z  z   |z         z
  |t              | d| z  dz   z  k(  sJ y )Nza b c xTr}   rb   r^   )r   rI   r*   r   )r   r   r   rU   s       ro   test_issue_17751r    sl    T2JAq!Q!a%T1q51*QT/AaC"7!";<<aDAaCRSGTTTrn   c                      t        t        t              t        t              z  t	        d      t        z  t        z  z  t        t
              t        d      t        t              z  k(  sJ y rz  )rI   r   rY   r*   r   r   r   rm   rn   ro   test_issue_17792r    sD    1d1g%s1vax!m3Q;tAwtBx?OOOOrn   c                      t        t        t        t                    t        dd      dk(  sJ t        t        t        t                    t        dd      dk(  sJ y )Nr   rc   ri   r_   rb   )rI   r   r6   rU   rm   rn   ro   test_issue_18118r    sD    c!fq!S)R///c!fq!S)Q...rn   c                      t        t        t        t                    t        t        t                    z  t        dd      dk(  sJ y )Nr   r_   rb   )rI   r6   r*   rU   rm   rn   ro   test_issue_18306r    s0    T!Wd3q6l*Aq#6!;;;rn   c                      t        t        t        dt        z        t        z         t        t        t              t        dz  z         z  t        t              dk(  sJ y )Nrd   r  )rI   r   r   rU   r   rm   rn   ro   test_issue_18378r    s@    S1X\"3s1v3#77B?1DDDrn   c                      t        dt        d      dz  t        z  z
  dt        z  z  t        t              t        u sJ t        t         t        z  t        t              t        u sJ y )Nrb   r^   rd   )rI   r   rU   r   r   rm   rn   ro   test_issue_18399r    sO    !ad1fQh,!A#&2.#5551"q!R C'''rn   c                      t        t        t              dt        t              z  z  t        t
        d      t        t        t              dt        t              z  z  t        t
        d      k(  sJ y )Nr^   rc   r`   )rI   r7   rU   r*   r   r   rH   rm   rn   ro   test_issue_18442r    sN    Q!d2h-(!RS9U3q6APTUWPXMCZ\]_agj=kkkkrn   c                      t        t        t        t                    t        z  t        d      dk(  sJ t        t        t        t                    t        z  t        dd      dk(  sJ y )Nr   rb   rc   )rI   r   r   rU   rm   rn   ro   test_issue_18452r    sJ    SVaA&!+++SVaAs+q000rn   c                     t        t        t              dt        z  z  t        t              t	        t        t              dt        z  z  t        t        d      k(  sJ t        t        t              dt        z  z  t        t              t	        t        t              dt        z  z  t        t        d      k(  sJ t        t        t              dt        z  z  t        t              t	        t        t              dt        z  z  t        t        d      k(  sJ t        t        t              dz   dt        z  z  t        t              dk(  sJ t        t        t              dz   dt        z  z  t        t              dk(  sJ t        t        t              dz
  dt        z  z  t        t              t	        t        t              dz
  dt        z  z  t        t        d      k(  sJ t        t        t              dz   dt        z  z  t        t              t        dd      k(  sJ t        t        t              dz  dt        z  z  t        t              t        dt              k(  sJ t        t        t              dz  dt        z  z  t        t              t        dd      k(  sJ t        t        t              dz   dt        z  z  t        t               t        dt              k(  sJ t        t        t              dz  dt        z  z  t        t               t        dt              k(  sJ t        t        t              dz  dt        z  z  t        t               t        dt              k(  sJ y )Nrb   rc   r`   r^   r  r   )rI   r6   rU   r   rH   r2   r7   rM   rm   rn   ro   test_issue_18473r    se   Q!A#2&%A1q"#*NNNNQ!A#2&%A1q"#*NNNNQ!A#2&%A1q"#*NNNN#a&1*!$a,111#a&2+1%q"-222#a&1*!$a,s1vzQqS6I1bVY0ZZZZ#a&1*!$a,Aq0AAAA#a&!)qs#a,Ar0BBBB#a&!)qs#Q+{1a/@@@@#a&1*!$a"-Q1CCCC#a&!)qs#Q,Ar0BBBB#a&!)qs#a"-Q1CCCCrn   c                      t        dt        dt        z        z  t        dt        z        dz   z  dt        z  z  t        t              t        d      k(  sJ y Nr^   rd   rb   )rI   r   rU   r   rm   rn   ro   test_issue_18482r  .  sC    !C!H*c!A#hl+qs3Q;s1vEEErn   c            	         t        t        t              t        dt	        t              z
        z  t        d      t        d      k(  sJ t        t        t              t        dt	        t              z
        z  t        dd      t        d      k(  sJ t        t        t              t        dt	        t              z
        z  t        dd      t        d       k(  sJ y )Nrb   r   r^   r_   r`   rc   )rI   r6   rU   r*   r2   rm   rn   ro   test_issue_18508r
  2  s    QQs1vX&1-a888QQs1vX&1#6$q'AAAQQs1vX&1#647(BBBrn   c                  &    t        t        d        y )Nc                  Z    t        t        dt        z
  t        z        t        t              S r   )rI   r   rY   rU   r   rm   rn   ro   r   z"test_issue_18521.<locals>.<lambda>9  s    c1q5A+.>2(F rn   r!  rm   rn   ro   test_issue_18521r  8  s    
 FGrn   c                      t        dd      \  } }t        t        |       | |      t        |      k(  sJ t        t        t        |             | |      t        t        |            k(  sJ y )Nr  Tr}   )r   rI   r   r   r  s     ro   test_issue_18969r  <  sZ    54(DAq!a#x{222Xa[!1a(C,<<<<rn   c                      t        t        t        t              dt        z  z  z  t        t              t	        d      k(  sJ y r.  )rI   rY   r   r   r   rm   rn   ro   test_issue_18992r  B  s/    IaL1Q3'(!R0CF:::rn   c                      t        d      } t        t        |       t        | dz
        t        | dz         z  z  | d      dk(  sJ y )NrU   rb   r^   r   ri   )r   rI   rC   r   s    ro   test_issue_19067r  F  s@    sAq5Q<a!e45q!<BBBrn   c                  j    t        t        dt        z  dt         z  z  z  t        t              dk(  sJ y r  rv   rm   rn   ro   test_issue_19586r  K  s,    QT!qb'\"Ar*a///rn   c                  ^    t        d      } t        dd      }t        | |z   | d      dk(  sJ y )NrY   r?  T)zeror   )r   rI   )rY   r?  s     ro   test_issue_13715r  O  s2    sAsAQ1"""rn   c            
          t        t        dz  t         dz
  t        dt        z        z  t        dz   t        dt        dz   z        z  z   z  t         dz   z  t        t              dk(  sJ y r  )rI   rY   r6   r   rm   rn   ro   test_issue_15055r  U  s\    AQAaC(AE3q!a%y>+AABQBFKQPRSWXXXXrn   c            
          t        dd      \  } }t        d      \  }}}t        ||z  |z  t        |       t        d|z  |z  |z  | |dz  z  z         z  z
  | |z  z   ||z  z  |d      |||z  z   |z  k(  sJ y )Nzm viTr}   zB ti drg   r^   r   )r   rI   r*   )r@  viBtir  s        ro   test_issue_16708r  Y  s    FT*EArx HAr1!B$r'DGDAaQQwY)>$???!B$F2NPQSTUZ[^`ac^cZcegYggggrn   c                  v   t        t        ddt        z        t        t        dt              dz  z  z  t        t              dt	        d      z  t
        z  dz  k(  sJ t        t        ddt        z        t        t        dt              dz  z  z  t        t               dt	        d      z  t
        z  dz  k(  sJ y )Nrb   rd   r^   rg   )rI   r8   rU   r   r*   r   rm   rn   ro   test_issue_19154r!  _  s    AqD!1gamQ&6#67R@Ad1gIbLQRNRRRAqD!1gamQ&6#67bSARQZPR]ST_TTTrn   c                  d   t        dd      } t        dd      }t        dd      }t        dd      }t        dd      }t        d      }d	|d
z  z  | z  |z  |d|z  | z  |z  z  z  }|d
z  |d
z  z  }||| z  |z  z  dz
  }| d|z  |z  z  |d
|z  |d
z  z  z  z
  |||| z  |z  z  dz   z  d
|z  |d	z  z  z  z
  |d|z  | z  |z  z  |z  z   }	t        t        |	      |        }
t	        |
d|z  |z  z
  | t
              dk(  sJ t	         |
j                         d|z  |z  z
  | t
              dk(  sJ y )NbetaTr}   hr@  omegarV  rb   rd   r^   r~   r   r   )r   r   r   r   rI   r   rK   )r#  r$  r@  wrV  r   qr?  r  Zr
   s              ro   test_issue_19453r)  d  sm   &4(DsT"AsT"Aw&AsT"AAA	!Q$tAa#a%*Q,''A	1QT	A	AdF1HA	
AaCE
Q!AqD\!Aq1T6!8}q'8$91Q3q!t8$DD#a%*Q,!	"A	c!fd	ASU1WdB'1,,,Aa'r2a777rn   c                  `    t        t        d       dz  t        z  t        t              dk(  sJ y )Nrb   r   r   r  rm   rn   ro   test_issue_19739r+  w  s'    1Q4%'Aq"%***rn   c                  z    t        dt         z  t        dt        dz   z  dz         z  t        t              dk(  sJ y )Nr^   r   rb   )rI   rU   r*   r   rm   rn   ro   test_issue_19766r-  {  s5    aRa!a%j1n--q"5:::rn   c                     t        d      } t        t        | t        z        t        z  t        t              t        t        | t        z        t        z  t        t        d      k(  sJ t        dd      } t        t        | t        z        t        z  t        t              t        t        | t        z        t        z  t        t        d      k(  sJ t        dd      } t        t        | t        z        t        t              t        dd      k(  sJ t        t        | t        z        t        z  t        t              d	k(  sJ y )
Nr@  rc   r`   Tr   )nonzerori   rb   r   )r   rI   r2   rU   r   rH   rM   )r@  s    ro   test_issue_19770r0    s    sAQqS!Q#uS1XaZBC'HHHHsAQqS!Q#uS1XaZBC'HHHHsD!AQqS1b![Q%7777QqS!Q#q(((rn   c            	         t        t        t              t        t        t                    z  t        t        dz        t        t        t              t        t        t                    z  t        t        dz  d      k(  sJ t        t        t              t        t        t                    z  t        t        dz  d      t        t        t              t        t        t                    z  t        t        dz  d      k(  sJ t        t        t              t        t        t                    z  t        t        dz  d      t        t        t              t        t        t                    z  t        t        dz  d      k(  sJ t        t        t        t                    t        t        dz        t        dd      k(  sJ t         dt        t               z  z  t        t         t              k(  sJ t        dt        t              z  z  t        t         t              k(  sJ t        dt        t               z  z  t        t         t              k(  sJ t         dt        t              z  z  t        t         t              k(  sJ y )Nr^   r_   r`   rc   rf   ri   rb   )rI   r7   rU   r6   r   rH   rM   r   rm   rn   ro   test_issue_7535r2    s   QCF#Q1-s1vc#a&k7I1bQRdX[1\\\\QCF#Q1#6%As3q6{@RTUWYZ[W[ad:eeeeQCF#Q1$75QCPQFASUVXZ[\X\bf;ggggSVQr!t$B(::::3#rc(
{B33333qRy>["b1111qbSz?k2#r22223#b'	?k2#r2222rn   c                  ~    t        t        dz   dt        z  z  t        z
  t        z  t        d      t         dz  k(  sJ y )Nrb   r   r^   )rI   rU   r
   rm   rn   ro   test_issue_20365r4    s5    1q5AaC.1$a'A.1"Q$666rn   c                      t        dt        z   dt        z  z  ddt        z  z   ddt        z  z  z  z
  t        t              z  t        d      t        dz  k(  sJ y )Nrb   r^   r   )rI   rU   r0   r
   rm   rn   ro   test_issue_21031r6    sL    1q5AaC.A!Gq!A#w#77a@!QG1Q3NNNrn   c                      t        t        t        t        z        dt        z  dz
  z  t        d      t        dz  k(  sJ y )Nrd   r   r   )rI   r6   r   rU   rm   rn   ro   test_issue_21038r8    s2    RTAaC"H%q!,1444rn   c                      t        t              t        dt        z        z  } t        | t        dd      dk(  sJ t        | t        dd      dk(  sJ t        | t        dd      dk(  sJ y )Nrb   r   r_   rc   rf   )r   rU   r6   rI   r   s    ro   test_issue_20578r:    sc    q6C!HDa#!###a#!###a$1$$$rn   c                     t        t              } | j                  t        t              t        k(  sJ | j                  t        t               t         k(  sJ t        t        t                     } | j                  t        t              t        t               k(  sJ | j                  t        t               t        t              k(  sJ t        t        t                    } | j                  t        t              t        t              k(  sJ | j                  t        t               t        t               k(  sJ | j                  t        t              t        t              k(  sJ t        t        t        dt        z                    } | j                  t        t              t        t        t                     k(  sJ | j                  t        t               t        t        t                    k(  sJ | j                  t        t              t        t        t                     k(  sJ | j                  t        t               t        t        t                    k(  sJ y )N)logxrb   )r   rU   nseriesrV   r7  s    ro   test_issue_21227r>    s   AA99QQ91$$$99QaR9 QB&&&SVGA99QQ93r7***99QaR9 CF***CFA99QQ93q6)))99QaR9 CG+++99QQ93q6)))CAaCMA99QQ93sA2w<///99QaR9 CAK///99QQ93sA2w<///99QaR9 CAK///rn   c                      t         dz
  t        dt         dz
  z        z  }  | j                  t         d      dk(  sJ  | j                         j                  t         d      dk(  sJ y r   )rU   r2   rI   r  )r   s    ro   test_issue_21415r@    sY    Q3AqsG
C399Qq>Q3::<a"a'''rn   c                      t        t        t        dz         t        t              z  t        t              t        k(  sJ y r.  )rI   r$   rY   r   r
   rm   rn   ro   test_issue_21530rB    s*    a!eT!W$a,111rn   c                      t        d      dz
  dz  } t        t        | z
  t        dz  t        z   dz
  z  t        |       t        d      dz  k(  sJ y )Nre   rb   r^   )r*   rI   rU   r  s    ro   test_issue_21550rD    sG    	a1aA!a%!Q$(Q,'A.$q'!);;;rn   c                      t        t        t        dz   z  t        t              dz   z  dz   t        z  t        d      } | t        d      dz  dt        d      z  z   k(  sJ y )Nrb      l   qjl   S[	)rI   rU   r   r   )outs    ro   test_issue_21661rH    sU    
QUs1vz*Q.!3Q
;C!M"2%SW(<<<<<rn   c                      t        t        t        t              t        t        z  z  j	                  t        d      t        d      t        d      dz  k(  sJ y )Nr   r   rb   i 	 )rI   r:   rW   rU   rD  r   rm   rn   ro   test_issue_21701rJ    s=    '!Q-1$**1a0!Q71Q4;FFFrn   c                      t        dd      } t        dt        dt        | z
  dz  z   z  z  t              } |j                  t        t
              t        j                  k(  sJ y )Nr   Tr   rb   r^   )r   rG   r   rU   rI   r   r   r   )r   r   s     ro   test_issue_21721rL    sN    sA!Ra!eaZ()1-A1771b>QVV###rn   c                     dt        dt        z  t        z  t        z        z
  dt        dt        z  t        z  t        z  dz        z
  z  } | j	                  t        d      dk(  sJ t        |       j	                  t        d      dk(  sJ y )Nrb   rg   re   r   )r   r   r   rW   rI   r   )terms    ro   test_issue_21756rO    sq    BqDGAISAb1%5!56D::aq   d8>>!Q1$$$rn   c                      t        d      } t        | dz   t        dz  z   dt        dz  z
  z        j                  | dd      t        k(  sJ y )Nr   r^   rb   rc   )r   r*   rU   rI   r   rG  s    ro   test_issue_21785rQ    sH    sA!Q$AAqD)*00As;q@@@rn   c                  \    t        dt        z  dt         z  z  t        t              dk(  sJ y )Nri   r^   r   rv   rm   rn   ro   test_issue_22181rS    s(    "q1r7"Ar*a///rn   c            	      
   t        d      t        t        d      t        t        dz        z  dz        z  dz  } t        d      t        z  t        t        d      t        t        dz        z  dt        d      z  t        z  dz  z
         t        t        d      t        t        dz        z  dt        d      z  t        z  dz  z         z   z  dz  }t        | t        t               t        d       t        z  dz  k(  sJ t        |t        t               t        d       t        z  dz  k(  sJ t        | t        t         d      t        d      t        z  dz  k(  sJ t        |t        t         d      dk(  sJ t        t        t        z
        t        t         t        z
        z
  }t        |d	
      }t        |t        t              t        |t        t              cxk(  rt        t        z  k(  sJ  J t        t        t        dz        t        z
         t        t        t        dz        t        z         z   x}}t        |t        t        d      dt        z  t        z  k(  sJ t        |t        t        d      dk(  sJ y )Nr  r^   r   r;  re   <   rc   r   T)forcer_   )
r*   r1   r7   rU   r   r   rI   r   rJ   r   )e1e2r   expr2s       ro   test_issue_22220rZ    s   	b$tBxAaC(*+	+B	.B	b!c$q'#ac(*QtBxZ\!^;<<$q'#ac(*QtBxZ\!^;<<= 
>>@
AB Qb	"R///Qb	"R///QS!T"Xb[^333QS!Q&&& q1u:QBF#Dt4(Eq"ua!4<"<<<<< AaC1%%s3qs8a<'889D4q"c"ac"f,,,q"c"a'''rn   c                     t        dd      \  } }t        |dz   | z  |dz   | dz   z  || dz   z  z
  z  |t              d| dz   z  k(  sJ t        |dz   | z  |dz   | dz   z  || dz   z  z
  j                         z  |t              d| dz   z  k(  sJ t        |dz   | z  ||| z   |dz   | z  z   z  |dz   | z  z   z  |t              d| dz   z  k(  sJ y )Nzk, nTr}   rb   )r   rI   r   r  )rX   rY   s     ro   test_issue_22334r\    s    FT*DAq!A#AaC1Q3<1!*45q"=AEJJJ!A#AaC1Q3<1!*4<<>>2F!QQRU)SSS!A#1q!teq1uqj01QUQJ>?BG1aRSe9TTTrn   c                      t        t        ddt        z  z         t        t              z  t        t              t        d      k(  sJ y rz  )rI   r   rU   r*   r   rm   rn   ro   test_sympyissue_22986r^    s2    q1Q3wQ'B/47:::rn   c                      dt         z  dt          z  z
  dt         z  dt          z  z   z  } t        | t         t               dk(  sJ y )Nr^   ri   )rU   rI   r   r7  s    ro   test_issue_23231r`    sA    	
AQB!Q$aR.)AAsr!!!rn   c                      t        dt        z   t        dz  z  t        dt        z        z  t        dt        f      t        k(  sJ y )Nrb   r^   ri   r   )rG   rU   r   r   rm   rn   ro   test_issue_23596rb    s6    q1uadlC1I-1bz:b@@@rn   c                     t        t         t        dz  z  t        z   dz
        } t        t         t        dz  z  t        t        z  z   dz
        }t        | t        dd      t        d       t        z  k(  sJ t        | t        dd      t        d       t        z  k(  sJ t        |t        dd      t        d      t        z  k(  sJ t        |t        dd      t        d       t        z  k(  sJ y )Nr^   rd   r   r_   rc   )r*   r   rU   rI   )expr1rY  s     ro   test_issue_23752re    s    !AqD1q!E!AqD1Q3"#E1c"tAwhqj0001c"tAwhqj0001c"d1gai///1c"tAwhqj000rn   c                     t        t        t        dz  t        t              z              j                  t              } | j                  t        t              dk(  sJ | j                         j                  t        t              dk(  sJ | j                  t              j                  t        t              dk(  sJ | j                  t              j                         j                  t        t              dk(  sJ y r   )r   r7   r   r#   rU   r   rI   r   rK   r   r6   )r  s    ro   test_issue_24276rg  "  s    	SAd1g		$	$Q	'B88Ar?a;;=q"%***::c?  B'1,,,::c?##%++Ar2a777rn   c                     t        dd      t        dd      } t        dd      }t        dd	      }t        t        fd
       t        t	        t
        |       t
        || z  d      dk(  sJ t        t	        t
        |       t
        || z  d      | k(  sJ t        t	        t
        |      t
        ||z  d      |k(  sJ t        t	        t
        |      t
        ||z  d      dk(  sJ y )Nr   Tr   r   r}   r   rA  rY   ro  c                  B    t        t        t               t               S r   )rI   r	   rU   rG  s   ro   r   z"test_issue_25230.<locals>.<lambda>.  s    c!QiA(> rn   r_   r   rc   )r   rR   r"  rI   r	   rU   )r   r   rY   r   s      @ro   test_issue_25230rj  )  s    s4 Ast$Ast$Asd#A
 >?QAqsC(A---QAqsC(A---QAqsC(A---QAqsC(A---rn   c                     t        t        t        t                    t        t        d      t         t
        z  k(  sJ t        t        t        t                    t        t        d      t        t
        z  k(  sJ t        t        t        t                    t        t        d      t        dz  k(  sJ t        t        t        t                    t        t        d      dk(  sJ t        t        t        t                    t        t        d      t        dz  k(  sJ t        t        t        t                    t        t        d      dk(  sJ y )Nrc   r^   r   )rI   r0   r   rU   r   r   r,   r1   r   r-   r/   r.   rm   rn   ro   test_issue_25582rl  5  s    c!fq"c*rc!e333c!fq"c*bd222c!fq"c*bd222c!fq"c*a///c!fq"c*bd222c!fq"c*a///rn   c                     t        t        t        t              t        z        t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t        t        t              t        z        t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      t         t        z  k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t        t        t              t        z        t        dd      dk(  sJ t        t        t        dt        z              t        dd      t        t        z  k(  sJ t        t        t        dt        z              t        dd      t        dz  k(  sJ t        t        t        t              t        z        t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t        t        dt        z              t        dd      t        dz  k(  sJ t        t        t        t              t        z        t        dd      dk(  sJ t        t        t        dt        z              t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      t        t        z  k(  sJ t        t        t        t              t        z        t        dd      t        dz  k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t        t        dt        z              t        dd      t         t        z  k(  sJ t        t        t        t              t        z        t        dd      t        k(  sJ t        t        t        dt        z              t        dd      t         t        z  dz  k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t        t        t              t        z        t        dd      t        dt!        d      z         k(  sJ t        t        t        dt        z              t        dd      t        k(  sJ t        t        t        dt        z              t        dd      dk(  sJ t        t#        t        t              t        z        t        dd      dk(  sJ t        t#        t        dt        z              t        dd      t        k(  sJ t        t#        t        dt        z              t        dd      t        t        z  dz  k(  sJ t        t%        t        t              t        z        t        dd      t        k(  sJ t        t%        t        dt        z              t        dd      dk(  sJ t        t%        t        dt        z              t        dd      t         t        z  dz  k(  sJ t        t'        t        t              t        z        t        dd      dk(  sJ t        t'        t        dt        z              t        dd      t        t        z  dz  k(  sJ t        t'        t        dt        z              t        dd      t        k(  sJ t        t)        t        t              t        z        t        dd      t        dt!        d      z         k(  sJ t        t)        t        dt        z              t        dd      dk(  sJ t        t)        t        dt        z              t        dd      t        k(  sJ y )Nr   rf   r   rb   r_   r^   rc   )rI   r1   r6   rU   r   r   r0   r   r   r,   r-   r/   r.   r   r   r   r*   r   r    r"   r!   rm   rn   ro   test_issue_25847rn  ?  s   c!fQhAt,1444c!A#hAs+r!t333c!A#hAs+q000 c!fQhAt,1444c!A#hAs+s1u444c!A#hAs+q000 c!fQhAt,111c!A#hAs+r!t333c!A#hAs+r!t333 c!fQhAt,1444c!A#hAs+q000c!A#hAs+r!t333 c!fQhAt,111c!A#hAs+r!t333c!A#hAs+r!t333 c!fQhAt,1444c!A#hAs+q000c!A#hAs+s1u444 s1vax!Q-333s1Q3x!Q,2a777s1Q3x!Q,111 s1vax!Q-Qa[1AAAAs1Q3x!Q,222s1Q3x!Q,111 s1vax!Q-222s1Q3x!Q,222s1Q3x!Q,"Q666 s1vax!Q-333s1Q3x!Q,111s1Q3x!Q,2a777 s1vax!Q-222s1Q3x!Q,"Q666s1Q3x!Q,222 s1vax!Q-Qa[1AAAAs1Q3x!Q,111s1Q3x!Q,222rn   c                      t        t        dt        dz         t        dt              z  t        t              t        j
                  k(  sJ y r  )rI   r8   rU   r   r   r   rm   rn   ro   test_issue_26040rp  }  s3    AE"71a=0!R8AFFBBBrn   c                     t        dt        z  t        dz  dt        z  z   dz   z        } t        dt        z  t        dz  dt        z  z   dz   z        }ddt        dz  z  z
  | dz  z  dz  t        dz  dt        z  z
  dz   | z  |z  dz  z
  }t        dz  t        dz  dt        dz  z  z
  t        dz  z
  dt        dz  z  z   t        dz  z
  dt        dz  z  z
  t        dz  z   z  }t	        ||z  t        d	      t        d       dz  k(  sJ y )
Nr   r^   rb   rd   ry   r   r   re   r   )rS   rU   rT   r   rI   r   )r   rX   rW  rX  s       ro   test_issue_26250rr    s   1Q31qs
Q'(A1Q31qs
Q'(AQq!tV8QT/!
q!tAaCxz1nQ.q0
0B	Q1qAv1$qAv-14qAv=1D	EBB1!A$q(((rn   N(   	itertoolsr   sympy.concrete.summationsr   sympy.core.functionr   r   
sympy.corer   r   sympy.core.modr	   sympy.core.numbersr
   r   r   r   r   r   sympy.core.singletonr   sympy.core.symbolr   r   %sympy.functions.combinatorial.numbersr   (sympy.functions.combinatorial.factorialsr   r   r   $sympy.functions.elementary.complexesr   r   r   &sympy.functions.elementary.exponentialr   r   r   %sympy.functions.elementary.hyperbolicr   r   r   r    r!   r"   r#   r$   #sympy.functions.elementary.integersr%   r&   r'   (sympy.functions.elementary.miscellaneousr(   r)   r*   $sympy.functions.elementary.piecewiser+   (sympy.functions.elementary.trigonometricr,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   sympy.functions.special.besselr8   r9   r:   r;   'sympy.functions.special.error_functionsr<   r=   r>   r?   r@   rA   'sympy.functions.special.gamma_functionsrB   rC   rD   sympy.functions.special.hyperrE   sympy.integrals.integralsrF   rG   sympy.series.limitsrH   rI   sympy.simplify.simplifyrJ   rK   sympy.simplify.hyperexpandrL   !sympy.calculus.accumulationboundsrM   sympy.core.mulrN   rO   sympy.series.orderrP   sympy.testing.pytestrQ   rR   sympyrS   rT   	sympy.abcrU   rV   rW   rX   rY   rp   rt   rw   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r
  r  r  r  r  r  r  r  r#  r*  r,  r/  r2  r5  r8  r=  rE  rH  rJ  rL  rN  rP  rS  rW  rZ  r\  r^  ra  re  rg  ri  rk  rm  rr  rt  rv  rx  r{  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r  r  r!  r)  r+  r-  r0  r2  r4  r6  r8  r:  r>  r@  rB  rD  rH  rJ  rL  rO  rQ  rS  rZ  r\  r^  r`  rb  re  rg  rj  rl  rn  rp  rr  rm   rn   ro   <module>r     s}    ) 0 .  < < " / ; X X @ @ G G h h h F F L L :Z Z Z Z O O ] ] P P 1 ; . : 2 9  * $ . (    
3t,D8N2,
A;S
$6/D124W&67 4A3>H@;
1.,2 # #9:>0
,"
*0(5*6
	6B7D - -A
8
A
M
@**K
 . ..
->`4@+$"?8T,
D;
3	2/S-A
-
L<7
F-B7L1-D
	RI
;J
BBIdo0B:[>.J%!F@:;4(* ( (
7SG
X\;TDNBU
P/
<E(
l1
D FCH=;C
0#YhU
8&+;	)37O5%02(2<
=
G$%A
0(,U;"
A18	.0;3|C)rn   